{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Your first Edward program\n",
    "\n",
    "Probabilistic modeling in Edward uses a simple language of random variables. Here we will show a Bayesian neural network. It is a neural network with a prior distribution on its weights.\n",
    "\n",
    "A webpage version is available at \n",
    "http://edwardlib.org/getting-started."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "from __future__ import absolute_import\n",
    "from __future__ import division\n",
    "from __future__ import print_function\n",
    "\n",
    "import edward as ed\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import tensorflow as tf\n",
    "\n",
    "from edward.models import Normal\n",
    "\n",
    "plt.style.use('ggplot')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def build_toy_dataset(N=50, noise_std=0.1):\n",
    "  x = np.linspace(-3, 3, num=N)\n",
    "  y = np.cos(x) + np.random.normal(0, noise_std, size=N)\n",
    "  x = x.astype(np.float32).reshape((N, 1))\n",
    "  y = y.astype(np.float32)\n",
    "  return x, y\n",
    "\n",
    "\n",
    "def neural_network(x, W_0, W_1, b_0, b_1):\n",
    "  h = tf.tanh(tf.matmul(x, W_0) + b_0)\n",
    "  h = tf.matmul(h, W_1) + b_1\n",
    "  return tf.reshape(h, [-1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, simulate a toy dataset of 50 observations with a cosine relationship."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "ed.set_seed(42)\n",
    "\n",
    "N = 50  # number of data points\n",
    "D = 1   # number of features\n",
    "\n",
    "x_train, y_train = build_toy_dataset(N)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, define a two-layer Bayesian neural network. Here, we define the neural network manually with `tanh` nonlinearities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "W_0 = Normal(loc=tf.zeros([D, 2]), scale=tf.ones([D, 2]))\n",
    "W_1 = Normal(loc=tf.zeros([2, 1]), scale=tf.ones([2, 1]))\n",
    "b_0 = Normal(loc=tf.zeros(2), scale=tf.ones(2))\n",
    "b_1 = Normal(loc=tf.zeros(1), scale=tf.ones(1))\n",
    "\n",
    "x = x_train\n",
    "y = Normal(loc=neural_network(x, W_0, W_1, b_0, b_1),\n",
    "           scale=0.1 * tf.ones(N))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, make inferences about the model from data. We will use variational inference. Specify a normal approximation over the weights and biases."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "qW_0 = Normal(loc=tf.get_variable(\"qW_0/loc\", [D, 2]),\n",
    "              scale=tf.nn.softplus(tf.get_variable(\"qW_0/scale\", [D, 2])))\n",
    "qW_1 = Normal(loc=tf.get_variable(\"qW_1/loc\", [2, 1]),\n",
    "              scale=tf.nn.softplus(tf.get_variable(\"qW_1/scale\", [2, 1])))\n",
    "qb_0 = Normal(loc=tf.get_variable(\"qb_0/loc\", [2]),\n",
    "              scale=tf.nn.softplus(tf.get_variable(\"qb_0/scale\", [2])))\n",
    "qb_1 = Normal(loc=tf.get_variable(\"qb_1/loc\", [1]),\n",
    "              scale=tf.nn.softplus(tf.get_variable(\"qb_1/scale\", [1])))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Defining `tf.get_variable` allows the variational factors’ parameters to vary. They are initialized randomly. The standard deviation parameters are constrained to be greater than zero according to a [softplus](https://en.wikipedia.org/wiki/Rectifier_(neural_networks)) transformation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Sample functions from variational model to visualize fits.\n",
    "rs = np.random.RandomState(0)\n",
    "inputs = np.linspace(-5, 5, num=400, dtype=np.float32)\n",
    "x = tf.expand_dims(inputs, 1)\n",
    "mus = tf.stack(\n",
    "    [neural_network(x, qW_0.sample(), qW_1.sample(),\n",
    "                    qb_0.sample(), qb_1.sample())\n",
    "     for _ in range(10)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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MdXU13/72t/nxj3/Mz3/+c+644w7m9+i7dffdd/PFL36RL3V580tKSli9evWIvgYhxNhm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\nIYQQQmyg/x/VawcuUPn0dgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1131e0e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# FIRST VISUALIZATION (prior)\n",
    "\n",
    "sess = ed.get_session()\n",
    "tf.global_variables_initializer().run()\n",
    "outputs = mus.eval()\n",
    "\n",
    "fig = plt.figure(figsize=(10, 6))\n",
    "ax = fig.add_subplot(111)\n",
    "ax.set_title(\"Iteration: 0\")\n",
    "ax.plot(x_train, y_train, 'ks', alpha=0.5, label='(x, y)')\n",
    "ax.plot(inputs, outputs[0].T, 'r', lw=2, alpha=0.5, label='prior draws')\n",
    "ax.plot(inputs, outputs[1:].T, 'r', lw=2, alpha=0.5)\n",
    "ax.set_xlim([-5, 5])\n",
    "ax.set_ylim([-2, 2])\n",
    "ax.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, run variational inference with the [Kullback-Leibler](https://en.wikipedia.org/wiki/Kullback–Leibler_divergence) divergence in order to infer the model’s latent variables with the given data. We specify `1000` iterations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\r",
      "1000/1000 [100%] ██████████████████████████████ Elapsed: 12s | Loss: -5.755"
     ]
    }
   ],
   "source": [
    "inference = ed.KLqp({W_0: qW_0, b_0: qb_0,\n",
    "                     W_1: qW_1, b_1: qb_1}, data={y: y_train})\n",
    "inference.run(n_iter=1000, n_samples=5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, criticize the model fit. Bayesian neural networks define a distribution over neural networks, so we can perform a graphical check. Draw neural networks from the inferred model and visualize how well it fits the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ysLKyiF56KXZWFr61a/Hu3g1AfMwYYkuWQCRC+q234t21CyIRt8RBaqobrBQF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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x115c90450>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# SECOND VISUALIZATION (posterior)\n",
    "\n",
    "outputs = mus.eval()\n",
    "\n",
    "fig = plt.figure(figsize=(10, 6))\n",
    "ax = fig.add_subplot(111)\n",
    "ax.set_title(\"Iteration: 1000\")\n",
    "ax.plot(x_train, y_train, 'ks', alpha=0.5, label='(x, y)')\n",
    "ax.plot(inputs, outputs[0].T, 'r', lw=2, alpha=0.5, label='posterior draws')\n",
    "ax.plot(inputs, outputs[1:].T, 'r', lw=2, alpha=0.5)\n",
    "ax.set_xlim([-5, 5])\n",
    "ax.set_ylim([-2, 2])\n",
    "ax.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The model has captured the cosine relationship between $x$ and $y$ in the observed domain.\n",
    "\n",
    "\n",
    "To learn more about Edward, [delve in](http://edwardlib.org/api)!\n",
    "\n",
    "If you prefer to learn via examples, then check out some\n",
    "[tutorials](http://edwardlib.org/tutorials/)."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
